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Parabolic Systems with Polynomial Growth and Regularity (Memoirs of the American Mathematical Society, 214)

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Date: 14 Feb 2017 16:02:45
Parabolic Systems with Polynomial Growth and Regularity (Memoirs of the American Mathematical Society, 214)

Parabolic Systems with Polynomial Growth and Regularity (Memoirs of the American Mathematical Society, 214) by Frank Duzaar
English | 2011 | ISBN: 0821849670 | 118 Pages | PDF | 967.71 KB

The authors establish a series of optimal regularity results for solutions to general non-linear parabolic systems $u_t- \mathrm{div} \ a(x,t,u,Du)+H=0,$ under the main assumption of polynomial growth at rate $p$ i.e. $|a(x,t,u,Du)|\leq L(1+|Du|^{p-1}), p \geq 2.$ They give a unified treatment of various interconnected aspects of the regularity theory: optimal partial regularity results for the spatial gradient of solutions, the first estimates on the (parabolic) Hausdorff dimension of the related singular set, and the first Calderon-Zygmund estimates for non-homogeneous problems are achieved here.
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